Modulus limit complication

lim as h->0 (|(h^2) + 4h |)/h comes out = 4 when i do it by splitting the definition of function according to modulus , but if according to distributive property of modulus , i can also write it as lim as h->0 (|h|/h)|((h) + 4|)) , but im as h->0 (|h|/h) does not exist , so whats wrong????????

lim as h->0 (|(h^2) + 4h |)/h comes out = 4 when i do it by splitting the definition of function according to modulus , but if according to distributive property of modulus , i can also write it as lim as h->0 (|h|/h)|((h) + 4|)) , but im as h->0 (|h|/h) does not exist , so whats wrong????????